|
The Nagel–Schreckenberg model is a theoretical model for the simulation of freeway traffic. The model was developed in the early 1990s by the German physicists Kai Nagel and Michael Schreckenberg. It is essentially a simple cellular automaton model for road traffic flow that can reproduce traffic jams, i.e., show a slow down in average car speed when the road is crowded (high density of cars). The model shows how traffic jams can be thought of as an emergent or collective phenomenon due to interactions between cars on the road, when the density of cars is high and so cars are close to each other on average. == Outline of the model == In the Nagel–Schreckenberg model, a road is divided into ''cells''. In the original model, these cells are aligned in a single row whose ends are connected so that all cells make up a circle (this is an example of what are called periodic boundary conditions). Each cell is either empty road or contains a single car; i.e., no more than one car can occupy a cell at any time. Each car is assigned a velocity which is an integer between 0 and a maximum velocity (= 5 in Nagel and Schreckenberg's original work). Time is discretized into time steps. This discretization in both space and time results in a cellular automaton. One can think of a cell as being a few car lengths long and the maximum velocity as being the speed limit on the road. The time step is then the time taken for a car at the speed limit to travel around 10 car lengths. However, the model can also be thought as just a way to understand or to model features of traffic jams by showing how interactions between nearby cars cause the cars to slow down. In each time step, the procedure is as follows.〔 In each step, the following four actions are conducted in order from first to last, and all are applied to all cars. In each action the updates are applied to all cars in parallel. # Acceleration: All cars not at the maximum velocity have their velocity increased by one unit. For example, if the velocity is 4 it is increased to 5. # Slowing down: All cars are checked to see if the distance between it and the car in front (in units of cells) is smaller than its current velocity (which has units of cells per time step). If the distance is smaller than the velocity, the velocity is reduced to the number of empty cells in front of the car – to avoid a collision. For example, if the velocity of a car is now 5, but there are only 3 free cells in front of it, with the fourth cell occupied by another car, the car velocity is reduced to 3. # Randomization: The speed of all cars that have a velocity of at least 1, is now reduced by one unit with a probability of p. For example, if p = 0.5, then if the velocity is 4, it is reduced to 3 50% of the time. # Car motion: Finally, all cars are moved forward the number of cells equal to their velocity. For example, if the velocity is 3, the car is moved forward 3 cells. These four actions are repeated many times, as long as is required to study any traffic jams that may form. The model is an example of an cellular automaton. The model is for a single lane where cars cannot pass each other; there is no overtaking. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Nagel–Schreckenberg model」の詳細全文を読む スポンサード リンク
|